Working Principle of Lithium ion Batteries

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    Lithium ion batteries essentially have the four major components viz, two electrodes (cathode, anode), separator and electrolyte. Two electrodes and separators are porous so that when filled with electrolyte, it is present all over the pores, while the two electrodes can also conduct electrons so that they reach the current collectors on which electrodes are coated. Since the electrodes are conducting, they need to be separated electrically and the separator here fulfills this task.

    In preparation of electrodes, carbon black is added for increasing electric conductivity while a binder for holding all the electrode tightly to the current collector.

    The main electrochemical activity of the cell happens at the electrodes, this activity is called as oxidation/reduction, during this process the lithium ions are either released or taken. If at one electrode oxidation takes place then at the other reduction takes place and thereby electrons also being released as a byproduct and we get current in this way. During this process ions need to move between electrodes and for this we have an electrolyte which has plenty of ions while the separator stops the flow of electrons between them from inside.

    While discharging the lithium ions move from anode to cathode since always ions which are negatively charged always move towards higher potential that is cathode, while charging we bias the anode towards higher potential thereby ions reverses it path back to anode. The cell potential is determined by the difference between the chemical potential of the lithium in the cathode and anode.

Electrochemistry - Oxidation and Reduction Reactions

    Oxidation and reduction always occur in pair, i.e., if oxidation occurs at one electrode then reduction takes place at other electrode. For example in a battery with $LiCoO_2$ as cathode and Carbon as anode, in discharging condition we have (oxidation is loss of electrons while reduction is gain of electrons)

    In terms of chemistry, the equations can be written as follows

Reduction at cathode: $CoO_2+Li^+ + e^- → LiCoO_2$

Oxidation at anode : $LiC_6 → C_6+Li^+ +e^-$
The complete reaction would be: $LiC_6+CoO_2  →  LiCoO_2+C_6$

Nernst equation
For anode, $E_a=E_a^°+{RT}/F.ln{[C_6][Li^+]}/{[LiC_6]}$

For cathode, $E_c=E_a^°+{RT}/F.ln{[CoO_2][Li^+]}/{[LiCoO_2]}$

where $E_c^°$ and  $E_a^°$ are the emf of cathode and anode wrt to lithium metal.

The overall voltage of the cell can be obtained when we consider the complete reaction,

$ΔE=E_c^°-E_a^°+{RT}/F.ln{[LiC_6][CoO_2]}/{[C_6][LiCoO_2]}$

This equations has essentially two terms, the first term which contains emf of cathode and anode while the second term with Ln and depends on the concentration of the products and reactants.

The voltage of a cell depend on both cathode and anode, and the value is equal to the difference between them.

First Term: $E_c^°-E_a^°$

    Each cathode and anode have different potential depending upon the chemistry, as can be seen from the figure. If we select a cell with LFP/LTO we have an voltage of (3.6-1.56) 2.04 V. For a different combination like LCO/Graphite we have (4.35-0.16) 4.19 V. Selection of chemistry is important depending upon applications and voltage is one of the important criteria since it directly affects the power density.

Second Term: $ln{[LiC_6][CoO_2]}/{[C_6][LiCoO_2]}$

    This term can be generalized into $ln{[Reactants]}/{[Products]}$. The value of this term decided the voltage of the cell in active mode i.e., charging or discharging. Most of understanding of lithium ion batteries depend on this reaction dynamics, where the profile of the voltage as the reaction progress is not linear but a curve which depend on the material chemistry.

    Generally in the specs sheet of cell, one can see the typical curve where we can see the overall voltage of the cell wrt to state of charge which is directly linked with progress of reaction. 0% SOC indicate the reaction is yet to start while 100% SOC indicate the reaction is completed for charging reaction and vice versa.  A typical overall voltage of the LCO/Graphite cell could be seen below.

Reversible process in lithium ion batteries:

1. Intercalation: The process of adding and removing lithium ions in a material without any significant changes in its structure is called as intercalation. Ex: LCO, Graphite, NMC, NCA, LFP, etc., There are bsically two categories of structures showing intercalation, layered structure  and 3D structures (spinel, olivine) and the volume change during the process is low.

2. Alloying: These materials form a bond with the lithium ions during charging and discharging. All of these class of materials act as anode Ex: Silicon, Tin, Germanium, etc. The structural changes are very drastic, like volume changes can go up to 300% which may lead to under-performance in battery.

3. Conversion reaction: These materials break and create new chemical bonds during during charging and discharging when Li insertion and extraction takes place. $Ex: Mn_3O_4,  FeF_2, FeS, CuCl_2, CoFe_2O_4$. Most of these materials show a moderte volumetric exapansion of around 10-30% and in some elemental S, Se and Te exhibit even more expansion upto 100%.